The 32-year-old has not played singles since losing in the first round of the Australian Open in January to Spain's Roberto Bautista Agut, after which he underwent hip resurfacing surgery in a bid to salvage his career.
France, who were 2-0 up courtesy of Arthur Rinderknech and Adrian Mannarino, faced little resistance from Ecuador as wins for Benjamin Bonzi and the doubles pair of Pierre-Hugues Herbert and Nicholas Mahut secured victory for the 10-times champions.
Although Kyrgios dropped the opening set his level of play and interest rose dramatically after the pep talk and he swept the next three sets for a 4-6, 7-6(6), 6-3, 6-0 win.
Serena Williams faces her first seeded opponent at the French Open on Thursday and will hope to use her booming serve to beat Australian Ashleigh Barty in the second round.
Germany's Jan-Lennard Struff and Tim Puetz pulled off a shock 6-3, 6-4, 3-6, 6-7(4), 7-5 win over Spain's Feliciano Lopez and Marc Lopez to give Germany a 2-1 lead in their Davis Cup quarter-final on Saturday.
Nicolas Mahut and Pierre-Hugues Herbert made sure of that with a gripping doubles win that keeps France's hopes against Croatia alive in the last final to be staged in the event's traditional format.
Croatia and France were tied at 1-1 after Friday's singles in their Davis Cup semi-final clash in Zadar after Richard Gasquet and Marin Cilic both won their matches.
The Swedish chair umpire who gave a pep talk to Australian Nick Kyrgios during a US Open match this year has been suspended without pay for two weeks, the ATP Tour said on Tuesday.
Sticking to a limited schedule has helped Roger Federer enjoy a renaissance late in his career but the Swiss says rest time is now over and he is looking forward to returning to action at the Mercedes Cup in Stuttgart.
Defending champion Petra Kvitova used a dominant serve to beat Lucie Safarova 6-7(6), 6-2, 6-2 in their all-Czech final at the Connecticut Open on Saturday.
Roger Federer began his pursuit for a sixth Swiss Indoors Basel title with an explosive 47-minute 6-2, 6-1 victory over Gilles Muller on Wednesday after Rafael Nadal reached the quarter-final with a 6-1, 6-1 win against Pierre-Hugues Herbert.
Tomic had to battle hard against the top seed, saving four match points in a tense final set before wrapping up the match in two hours and 15 minutes.
Favourites Russia Tennis Federation opened their Davis Cup Finals campaign with a resounding victory over Ecuador, Britain began with a win against France and Italy eased into the quarter-finals with a win over Colombia on Saturday.
Order of play on the main show courts at the French Open.
Japan Warriors did not have to break much sweat in getting past Philippine Marvericks 29-15 but it was a tough day out for UAE Royals, who edged out hosts Singapore Slammers 27-23 in their IPTL match, riding on Roger Federer's win in the deciding men's singles, in Singapore on Friday.
Serena Williams fuelled talk of a dream-team partnership with home favourite Andy Murray after declaring her availability for the Wimbledon mixed doubles.
UAE Royals notched up their second consecutive win with a comprehensive victory over home team Japan Warriors on the second day of the International Premier League Tennis on Thursday.
France won their 10th Davis Cup title when Lucas Pouille crushed Steve Darcis 6-3, 6-1, 6-0 to give the hosts a 3-2 victory in the final against neighbours Belgium on Sunday.
Belgium's chances of claiming a maiden Davis Cup title against hosts France remained intact after Friday's opening singles, in which David Goffin made a huge impression, were tied 1-1.
Hewitt, the 2001 champion, received his wildcard via a reciprocal agreement with Tennis Australia, which will grant an American a wild card into next year's Australian Open, and was among 16 players who received wildcard entries.
The United States Tennis Association (USTA) said on Sunday it would undertake a review of its communication policies after a string of umpiring controversies at the U.S. Open.
Serbia sealed their place in the Davis Cup quarter-finals in straightforward fashion but Britain survived another nail-biter before joining them in the last-eight on Thursday.
Marin Cilic sent Croatia into the Davis Cup final with a 6-3, 6-2, 7-5 victory against Richard Gasquet on Sunday that gave the hosts a 3-1 win over France.
Borna Coric and Marin Cilic put Croatia in complete control of the Davis Cup final on Friday, leaving hosts and defending champions France facing what looks like mission impossible.
It was a repeat of the 34-year-old's straight sets victory over Andy Murray in the second round of the US Open in August.
Konta, Sharapova fall at Rogers Cup in Toronto
Novak Djokovic extended his unbeaten start to the season to 15 matches as he swatted aside German veteran Philipp Kohlschreiber 6-3 6-1 with ease on Wednesday to reach the Dubai Tennis Championships quarter-finals.
Ramkumar Ramanathan enhanced his reputation of being a passionate fighter even in defeat against a much superior Marin Cilic while Yuki Bhambri squandered six break chances to crash out of the Tata Open Maharashtra in Pune on Wednesday.
British pair Jamie Murray and Dominic Inglot defeated Canadians Daniel Nestor and Vasek Pospisil in four sets in Ottawa to give Britain a 2-1 lead ahead of Sunday's reverse singles.
Defending champions Indian Aces bounced back in style to beat Singapore Slammers 27-20 and record their second successive win in the Japan leg of the International Premier Tennis League (IPTL) season 2 in Kobe.
Issues of sexism, officiating double standards and adverse playing conditions have dominated the 50th anniversary of the U.S. Open, raising uncomfortable questions and prompting authorities to promise a review of existing policies.
India's top singles player Yuki Bhambri and Asian Games gold-medallist Divij Sharan have pulled out of the Davis Cup World Group Play-off tie against Serbia due to injuries while Sumit Nagal has refused to join the team as a stand-by.
Novak Djokovic launched his bid to stay on course for a Golden Slam with a clinical 6-2, 6-2 win over 139th-ranked Hugo Dellien of Bolivia on Saturday, as sweltering conditions in Tokyo took a toll on the players on the opening day of tennis at the Games.
IMAGES from the matches played at the PNB Paribas Open at Indian Wells on Wednesday
Osaka survives test to reach last 16
Images from Day 2 of the French Open matches played at Roland Garros on Monday
Richard Gasquet kept his ATP World Tour finals hopes alive when he overcame Fernando Verdasco 7-5, 6-7(6), 6-3 to reach the Paris Masters third round as fellow Frenchman Jo-Wilfried Tsonga crashed out of the race on Tuesday.
Summary of sports events and persons who made news on Sunday
World number two Murray, who smashed a frame in anger in the final game, said the proximity of next week's Davis Cup final on a claycourt in Ghent had not been a factor in his defeat.
Images from Day 1 of the Wimbledon Championships.